Question

The summit of a mountain, 2450m above base camp, is measured on a map to be 4580m horizontally from the camp in a direction 32.4º west of north. what are the components of the displacement vector from camp to summit? what is its magnitude? choose the x axis east, y axis north and z axis up.

Answer 1

consider east-west direction along x-axis and north-south direction along y-axis

x = x- component of the displacement vector = - 4580 Sin32.4 = - 2454.1 m

y = y- component of the displacement vector = 4580 Cos32.4 = 3867.02 m

z = z-component of the displacement vector = 2450 m

magnitude of displacement vector is given as

magnitude = sqrt(x² + y² + z²) = sqrt((- 2454.1)² + (3867.02)² + (2450)²) = 5194.13 m